The area of a right triangle is 44 m². Find the lengths of its legs if one of the legs is 3 m longer than the other.

Answer:

[tex]y=3x^2+12x+17[/tex]

Step-by-step explanation:

The equation in vertex form is [tex]y=a(x+2)^2+5[/tex].

We can use the point [tex](1,32)[/tex] to solve for [tex]a[/tex].

[tex]32=a(1+2)^2+5 \\ \\ 27=9a \\ \\ a=3 \\ \\ \\ \therefore y=3(x+2)^2 + 5 \\ \\ =3(x^2+4x+4)+5 \\ \\ =3x^2+12x+12+5 \\ \\ =3x^2+12x+17[/tex]

Answer:

[tex]60-15\pi[/tex] square inches

Step-by-step explanation:

The area of the paper is [tex](6)(10)=60[/tex] square inches.

The area of one circle is [tex]\pi(1^2)=\pi[/tex]. So, the combined area of the circles is [tex]15\pi[/tex].

Taking the difference yields [tex]60-15\pi[/tex].

Answer: its A

Step-by-step explanation:

edge 2023

T-scores show how many standard deviation units an examinee's score differs from the mean. Because T-Scores have a mean of 50 and a standard deviation of 10, any T-Score may be directly interpreted.

A t-score (sometimes known as a t-value) is the number of standard deviations from the mean of the t-distribution. The test statistic used in t-tests and regression testing is the t-score. It may also be used to represent how distant an observation is from the mean when the data follows a t-distribution. A t test is a statistical test used to compare two groups' means. It is frequently used in hypothesis testing to assess whether a procedure or treatment has an effect on the population of interest, or whether two groups vary.

Here,

T-scores reflect how many standard deviation units an examinee's score is above or below the mean. Because T-Scores always have a mean of 50 and a standard deviation of 10, any T-Score may be directly interpreted.

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Answer:

Step-by-step explanation:

c=84

c+44 is going to be equal to the sum of c and c-40 because c+44 is the remote angle to both c-40 and c so you set it up as:

c + c - 40= c + 44

you simplify

2c - 40 = c + 44

you add 40 to both sides

2c = c + 84

you subtract c

and your answer is: c=84

The four types of transformations are Rotation, Translation, Dilation and Reflection

The term transformation in math is defined as  a process of changing the position of every point on a plane in a way that satisfies certain rules.

The four types of transformations are defined as,

1) Translation - It is the form of transformation to move each point the same distance and direction

2) Dilation - This type of transformation is to expands or contracts the shape

3) Rotation - This one will rotates each point in the shape at a certain number of degrees around that point

4) Reflection - It means that each point in the shape is reflected over a line

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Pizza left for me equal to 0.94 part

Both rates and ratios are a comparison of two numbers.

A rate is simply a specific type of ratio.

The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.

For example, in a room full of students, there are 10 boys and 5 girls. This means the ratio of boys to girls is 10:5.

If we simplify the ratio, we see that the ratio of boys to girls is 2:1, since

10÷5=2and 5÷5=1

. Thus, there are 2 boys in the room for every 1 girl.

A friend ate 1/100 part of pizza 6 times

Totally , He have eaten=  1/100 * 6

                                      =3/50

3/50 part of pizza he eaten = 0.06

Total pizza = pizza eaten + pizza left

pizza left = Total pizza - pizza eaten

               = 1 - 0.06

               = 0.94

pizza left for me equal to 0.94 part

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For example, in a room full of students, there are 10 boys and 5 girls. This means the ratio of boys to girls is 10:5.

If we simplify the ratio, we see that the ratio of boys to girls is 2:1, since

10÷5=2and 5÷5=1

Thus, there are 2 boys in the room for every 1 girl.

A friend ate 1/100 part of pizza 6 times

Totally , He have eaten=  1/100 * 6

=3/50

3/50 part of pizza he eaten = 0.06

Total pizza = pizza eaten + pizza left

pizza left = Total pizza - pizza eaten

              = 1 - 0.06

              = 0.94

pizza left for me equal to 0.94 part

The relationship between the volume of a prism and pyramid with congruent bases and heights is that the volume of pyramid is one-third of the volume of prism.

As the prism and pyramid have congruent bases and heights, let us consider the area of the triangular base is A and the height is h.

For a prism of base area A and height h, volume is determined by the formula

Vpm = A×h

For a pyramid of base area A and height h, volume is determined by the formula

Vpd = A×h/3

From both relations for volume

Vpd = Vpm/3

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Answer:

f(x)

Step-by-step explanation:

f(x) changes at a constant rate   when x changes from 1 to 2 the change in y = 7      when x changes from 2 to 3 the change in y = 7   etc

the others do not change at a constant rate when x changes by one

The data represented by table number one is showing the linear relation.

A linear relationship (or linear association) is a statistical term that describes a two-variable relationship that follows a straight line.

The momentum of a variable is represented by the rate of change, which is used to mathematically describe the percentage change in value over a defined period of time. If the rate of change is constant then the relationship will be linear.

For table number one the data is,

x    F(x)

1     12

2    19

3    26

4    33

The rate of change will be,

R₁ = ( 19 - 12 ) / ( 2 - 1 )  = 7

R₂ = ( 26 - 19 ) / ( 3 - 1 ) = 7

R₃ = ( 33 - 26 ) / ( 4 - 3 )= 7

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Using sample standard deviation formula and the provided sample mean value, The test statistic are $8,080(sample mean) and 125 (sample standard deviation).

Large-scale numerical data collection and analysis, especially with the aim of extrapolating proportions in the total from those in a representative sample.

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait.

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

Sample mean= $8,080

population standard deviation= $1,000

number of sample=64

sample standard deviation = [tex]\frac {1000}{\sqrt {64}}[/tex]

=1000/8

=125

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To graph a line with two independent variables, you can use a three-dimensional coordinate system. The three dimensions of the coordinate system are the two independent variables and the dependent variable.

For example, suppose you have a line described by the equation y = 2x + 3z + 4. In this equation, x and z are the independent variables and y is the dependent variable. To graph this line, you would need to plot points in three-dimensional space, using the values of x, y, and z from the equation.

To do this, you can choose specific values for x and z, substitute those values into the equation to find the corresponding value of y, and plot those three values as a point in three-dimensional space. You can repeat this process for several different values of x and z to plot multiple points on the line. Once you have plotted enough points, you can connect them with a line to graph the equation in three dimensions.

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Answer: x = 1, 7, vertex is at (4, -9)

Step-by-step explanation:

       To find the x-intercepts, we will factor and solve. Finding the x-intercepts is the same as finding the solutions, where f(x) = 0. -7 and -1 multiply to 7, and -7 + -1 = -8.

y = x² - 8x + 7

y = (x - 7)(x - 1)

x = 7       x = 1

       Next, we can use this equation to help us find the x-value of the vertex.

[tex]\displaystyle \frac{-b}{2a} =\frac{8}{2(1)} =\frac{8}{2} =4[/tex]

       Then, we will substitute this value back into the equation to solve for the y-value.

y = x² - 8x + 7

y = (4)² - 8(4) + 7

y = -9

   The vertex is at (4, -9)

The required height of the tub is given as 7.32 inches.

As mentioned in the question, Ice cream is packaged in cylindrical gallon tubs. A tub of ice cream has a total surface area of 387.79 square inches, and the diameter of the tub is 10 inches.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,
The surface area of the cylinder = 2πrh + 2πr²
Substitute the values,
387.79 = 2 × 3.14 × 5 [h + 5]
h = 7.32 inches

Thus, the height of the cylindrical gallon tub is given as 7.32 inches.

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Answer:

7.35 inches

Step-by-step explanation:

I took the test and got it right :)

False; we only remove outliers if we have a very good justification that suggests that removing the outlier is appropriate.

You should discard the outlier if it is clear that it resulted from inaccurately measured or recorded data. You may discard the outlier if it has no effect on the results but has an impact on the assumptions. Outliers might occasionally point to a data-gathering error. However, there are situations when they might have an impact on data collection, making them crucial to keep in mind in order to fully comprehend the information. Eliminating outliers gives some of my variables a normal distribution and improves the effectiveness of modifications for the other variables. As a result, it would appear that eliminating outliers before transformation is the best course of action.

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The AAS congruence rule states that if two angles and the included side of a triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.

The AAS congruence rule is a rule used in geometry to determine when two angles are congruent, or equal. This rule states that two angles are congruent if they are both angles of a triangle and they share the same side or vertex. This rule is a part of the Angle-Angle-Side (AAS) theorem, which states that three angles and three sides of one triangle are equal to three angles and three sides of another triangle.

To prove this congruence rule, we need to use the Side-Angle-Side (SAS) congruence theorem. This theorem states that if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent. This theorem can be used to prove the AAS congruence rule, as it states that if two angles and the included side of a triangle are congruent to the corresponding parts of another triangle, then they can be used to form two sides and the included angle of a new triangle, which satisfies the conditions of the SAS congruence theorem. Therefore, the two triangles are congruent, proving the AAS congruence rule.

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Answer:

Step-by-step explanation:Rearrange terms

3x-5+({5+6x})

Solution

9x     will that help?

Answer:

Step-by-step explanation:

(3x-5)+(5+6x)

3x-5+5+6x

3x+6x+5-5

3x+6x

9x

i think this is the right answer

A file that contains 154 megabytes occupies 22% of the available space.

We can calculate the percent of the space by using the following formula:

The percent of the space = used space / storage space × 100%

A CD-Rom holds 700 megabytes of data.

A file containing 154 megabytes occupies the space.

The percent of the space = used space / storage space × 100%

The percent of the space = 154 / 700 × 100%

The percent of the space = 0.22 × 100%

Apply the multiplication operation, and we get

The percent of the space = 22%

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Answer:

The rate of change/cost per mile driven can be calculated by finding the slope of the line that connects the points (1,10.70) and (0,10). The slope is the change in the y-value divided by the change in the x-value, so the slope of the line is (10.70-10)/(1-0) = $0.70/mile.

The point (0, 10) represents the cost of the driving service when 0 miles are driven. In other words, the service costs $10 for no miles driven.

The equation that models the function in the table is C(m) = $10 + $0.70m. The first term represents the cost of the service when no miles are driven and the second term represents the cost per mile driven.

The width of the interval will be is 5 or ( 49.5 , 54.5 ) .

Given :

The minimum value is called the lower class limit and the maximum value is called the upper class limit. For class interval 50-54, the lower class limit is 50 and the upper class limit is 54.

Class boundaries are the numbers used to separate classes. It is the real limits of a class. For non-overlapping classes, the lower class boundary of each class is calculated by subtracting 0.5 from the lower class limit. The upper class boundary of each class is calculated by adding 0.5 to the upper class limit.

Example: For class interval 50-54, the lower class boundary is 49.5 and the upper class class boundary is 54.5

Considering the question given, to get the real limits of the interval 50-54, 0.5 is subtracted from the lower class limit to give 49.5. Also, 0.5 is added to the upper class limit to give 54.5.

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the slope  is 5/-2 so this line "cuts" the y axis at y=-2.50000

y-intercept = 5/-2  = -2.5

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                   -2*y-(-4*x+5)=0

Pulling out like terms

Pull out like factors :

 -2y + 4x - 5  =   -1 • (2y - 4x + 5)

Equation at the end

Equation of a Straight Line

  Solve   -2y+4x-5  = 0

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  -2y+4x-5  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/-2 so this line "cuts" the y axis at y=-2.50000

y-intercept = 5/-2  = -2.5

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The system of Linear equations is; y = 7x + 3(6 - x) and the solution is;

7 scores from touchdowns

15 scores from field goals

Total score of 22

Let the number of touchdowns be x

Let the total of the home team points be y

Thus, the number of field goals = 6 - x since the team scores 6 times.

Thus, since the home team points are from 7 point touchdowns and 3 point field goals, then it means we have the equation;

y = 7x + 3(6 - x)

where;

7x is scores from touchdowns

3(6 - x) is scores from field goals

Thus;

y = 7x + 18 - 3x

y = 4x + 18

Let's try x = 1 and we have;

7(x) = 7(1) = 7 scores from touchdowns

3(6 - 1) = 15 scores from field goals

y = 4(1) + 18

y = 22

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Answer:

hello im ur friend and im going to give u the answer next year

Answer:

  no solution

Step-by-step explanation:

You want the solution to the radical equation √(2x+6) = -8.

The radical symbol is used to signify the positive square root. Whatever non-negative value (2x+6) may have, the left side expression returns a positive value for the root. It can never be equal to -8.

There is no solution to the given equation.

The 4 parts of a function are Function name, Parameters ,Body, Return statement.

1. Function name: This is the name of the function, which is used to identify the function and call it when needed. It should be descriptive, so that it is easy to understand what the function does.

2. Parameters: Parameters are values that are passed into the function when it is called. They are used to provide the function with the necessary data it needs to perform its task.

3. Body: This is the code that will be executed when the function is called. It contains the instructions that the function needs to perform its task.

4. Return statement: This is the statement that is used to return the result of the function. It can be used to return a value or object. It can also be used to return a status code, such as success or failure.

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Kate has encountered Simpson's Paradox because even though pepperoni pizza is the most popular flavor on weekdays.

Simpson's Paradox is the phenomenon that occurs when a trend appears to be in one direction when data is grouped in one way, but the trend is reversed when the data is grouped in another way.

In this case, Kate has encountered Simpson's Paradox because even though pepperoni pizza is the most popular flavor on weekdays, and again on the weekends when all the data is considered, the overall popularity of sausage pizza is greater.

Simpson's Paradox can be explained by the fact that the number of sausage pizza sales may be greater than the number of pepperoni pizza sales, even if the percentage of pepperoni pizza sales is higher.

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Kate has encountered the Simpson's Paradox. By definition, Simpson's Paradox is a phenomenon in which a trend appears in several different groups of data but disappears when these groups are combined. Option c is the right option

A relationship between two variables in a population might exist, vanish, or even change when the population is split up into subpopulations, a statistical phenomenon is known as Simpson's paradox.

Simpson's paradox is a statistical effect that arises when the marginal association between two categorical variables differs qualitatively from the partial association between the same two variables after adjusting for one or more other factors.

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The  expression used to represent the binomial theorem example is equal to ( 5 + 0.1 )⁴ .

As given in the question,

Example used to represents the binomial theorem is written as:

( 5 + 0.1 )⁴

Compare it with standard form and apply binomial theorem to simplify the considered example:

( a + b )ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+  ⁿCₙa⁰bⁿ

Here in the considered example :

value of a = 5

value pf b = 0.1

value pf n = 4

Substitute the value in the formula to get the value using binomial theorem:

( 5 + 0.1 )⁴

=  ⁴C₀5⁴(0.1)⁰ +  ⁴C₁5⁴⁻¹(0.1)¹ + ⁴C₂5⁴⁻²(0.1)² +  ⁴C₃5⁴⁻³(0.1)³ +  ⁴C₄5⁴⁻⁴(0.1)⁴

= 5⁴ + 4(5)³(0.1) + 6(5)²(0.1)² + 4(5)(0.1)³ + (0.1)⁴

= 625 + 50 + 1.5 + 0.02 + 0.0001

=676.5201

Therefore, the example of the binomial theorem is given by ( 5 + 0.1 )⁴.

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the distance between the chord is 23 cm

It is given that AB = 30cm and CD = 16cm

Join the lines OA and OC

We know that AO = 17cm and CO = 17cm

Construct OM ⊥ CD and OL ⊥ AB

The perpendicular from the centre of a circle to a chord bisects the chord

We know that

AL = ½ × AB

By substituting the values

AL = ½ × 30

So we get

AL = 15cm

We know that

CM = ½ × CD

By substituting the values

CM = ½ × 16

So we get

CM = 8cm

Consider △ ALO

Using the Pythagoras theorem it can be written as

AO^2 = OL^2 + AL^2

By substituting the values

17^2 = OL^2 + 15^2

So we get

OL^2 = 17^2 - 15^2

On further calculation

OL^2 = 289 – 225

By subtraction

OL^2 = 64

By taking the square root

OL = √64

OL = 8cm

Consider △ CMO

Using the Pythagoras theorem it can be written as

CO^2 = CM^2 + OM^2

By substituting the values

17^2 = 82 + OM^2

So we get

OM^2 = 17^2 - 8^2

On further calculation

OM^2 = 289 – 64

By subtraction

OM^2 = 225

By taking the square root

OM = √225

OM = 15cm

So the distance between the chords = OM + OL

By substituting the values

Distance between the chords = 8 + 15 = 23cm

Therefore, the distance between the chords is 23 cm.

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The value of the angle of the arc in the wheel is equal to 135. The correct option is D.

An arc of a circle is a section of the circle's circumference between two radii. A circle's central angle is an angle formed by two radii with the vertex in the centre. The central angle of an arc is the central angle that the arc subtends. The length of an arc is equal to the length of its central angle.

The angle suspended by the arc on the wheel is 3/8 that of the one revolution of the wheel.

The value of the angle will be calculated as,

Angle = 3/8 x 360

Angle = 3 x 45

Angle = 135

Therefore, the value of the angle of the arc in the wheel is equal to 135. The correct option is D.

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To solve systems of an infinite equation we need to determine whether the equation is dependent or independent and consistent, or inconsistent.

The number of solutions in an equation depends on the total number of variables contained in it is known as Infinite solutions.

The system of equations contains two or more equations that have two or more variables. It can be any combination such as

If a pair of linear equations have unique or infinite solutions, then the system of equations is said to be a consistent pair of linear equations.

For example, consider two equations in two variables as follows:

a1x + b1y = c1 ——- (1)

a2x + b2y = c2 ——- (2)

The above-given equations are consistent and dependent and have infinitely many solutions.

(a1/a2) = (b1/b2) = (c1/c2)

There are a few conditions for infinite solutions:

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